Surface reconstruction of anatomical structures is an integral part of medical modeling. Contour information is extracted from serial cross-sections of tissue data and is stored as "slice" files. Although there are several reasonably efficient triangulation algorithms that reconstruct surfaces from slice data, the models generated from them have a jagged or faceted appearance due to the large inter-slice distance created by the sectioning process. Moreover, inconsistencies in user input aggravate the problem. So, we created a method that reduces inter-slice distance, as well as ignores the inconsistencies in the user input. Our method called the piecewise weighted implicit functions, is based on the approach of weighting smaller implicit functions. It takes only a few slices at a time to construct the implicit function. This method is based on a technique called variational interpolation. <p> Other approaches based on variational interpolation have the disadvantage of becoming unstable when the model is quite large with more than a few thousand constraint points. Furthermore, tracing the intermediate contours becomes expensive for large models. Even though some fast fitting methods handle such instability problems, there is no apparent improvement in contour tracing time, because, the value of each data point on the contour boundary is evaluated using a single large implicit function that essentially uses all constraint points. Our method handles both these problems using a sliding window approach. As our method uses only a local domain to construct each implicit function, it achieves a considerable run-time saving over the other methods. The resulting software produces interpolated models from large data sets in a few minutes on an ordinary desktop computer.

Surface reconstruction of anatomical structures is an integral part of medical modeling. Contour information is extracted from serial cross-sections of tissue data and is stored as "slice" files. Although there are several reasonably efficient triangulation algorithms that reconstruct surfaces from slice data, the models generated from them have a jagged or faceted appearance due to the large inter-slice distance created by the sectioning process. Moreover, inconsistencies in user input aggravate the problem. So, we created a method that reduces inter-slice distance, as well as ignores the inconsistencies in the user input. Our method called the piecewise weighted implicit functions, is based on the approach of weighting smaller implicit functions. It takes only a few slices at a time to construct the implicit function. This method is based on a technique called variational interpolation. <p> Other approaches based on variational interpolation have the disadvantage of becoming unstable when the model is quite large with more than a few thousand constraint points. Furthermore, tracing the intermediate contours becomes expensive for large models. Even though some fast fitting methods handle such instability problems, there is no apparent improvement in contour tracing time, because, the value of each data point on the contour boundary is evaluated using a single large implicit function that essentially uses all constraint points. Our method handles both these problems using a sliding window approach. As our method uses only a local domain to construct each implicit function, it achieves a considerable run-time saving over the other methods. The resulting software produces interpolated models from large data sets in a few minutes on an ordinary desktop computer.

A novel idea for perception of object surfaces is presented by so called &quot;shape descriptors&quot;. Such idea is as an abstract level to represent the object surface by some real numbers. It has the similar idea like as the Fourier coefficients of mapping a function f(x) to frequency domain by Fourier transform. The main goal of this thesis is to define some of the key issues in understanding of an object shape and also to find a modeling methodology to create the &quot;shape descriptors&quot;. The modeling methodology is designed based on a variational interpolation technique. Such technique is used to generate a group of variational implicit functions with help of radial basis functions. In our modeling methodology, we randomly choose some reference points on a set of related concentric spheres around a 3D point cloud data as known values in variational implicit functions. The &quot;shape descriptors&quot; are found from these implicit functions implementing LU decomposition. We show that the &quot;shape descriptors&quot; are invariant to size and positioning (rotation and translation) changes of a shape and they are also effective tools for matching of two similar objects surfaces.